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Related Concept Videos

Variance01:15

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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
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Conducting a three-phase short circuit test on an unloaded synchronous machine helps understand its impact on the system. The AC fault current's oscillogram, with the DC offset removed, reveals that the waveform amplitude decreases from an initially high value to a steady-state level for one phase of the machine.
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Friedman's Two-Way Analysis of Variance by Ranks is a nonparametric test designed to identify differences across multiple test attempts when traditional assumptions of normality and equal variances do not apply. Unlike conventional ANOVA, which requires normally distributed data with equal variances, Friedman's test is ideal for ordinal or non-normally distributed data, making it particularly useful for analyzing dependent samples, such as matched subjects over time or repeated measures...
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Machines01:19

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Machines are complex structures consisting of movable, pin-connected multi-force members that work together to transmit forces. One example of a machine is the cutting plier, which is used to cut wires by applying forces to its handles. When equal and opposite forces are exerted on the handles of the cutting plier, they cause the cutting edges to come together and apply equal and opposite reaction forces on the wire, which are greater than the applied forces.
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Reporting and recording are crucial in data documentation. The timely, thorough, and accurate documentation of facts is essential when recording patient data. Failure to record findings during an assessment or interpretation of a problem will result in loss of information and make the patient document unreliable. The reader is left with general impressions if the information is not specific. A recording is documenting data of the individual's health information in a traceable, secure, and...
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What are Estimates?01:06

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It isn't easy to measure a parameter such as the mean height or the mean weight of a population. So, we draw samples from the population and calculate the mean height or mean weight of the individuals in the sample. This sample data acts as a representative measure of the population parameter. These sample statistics are known as estimates. 
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Machine learning based variance estimation under two phase sampling using health and education sector data.

Sanaa Al-Marzouki1, Ibrahim A Nafisah2, Mhassen E E Dalam3

  • 1Statistics Department, Faculty of Science, King Abdul Aziz University, Jeddah, Kingdom of Saudi Arabia.

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|February 7, 2026
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Summary
This summary is machine-generated.

This study introduces a new variance estimator for two-phase sampling, improving estimation efficiency using minimal auxiliary data. The novel method shows superior analytical and empirical performance compared to existing estimators.

Keywords:
And probability distributionAuxiliary informationHybrid modelingMachine learningTwo-phase samplingVariance estimation

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Area of Science:

  • Statistics
  • Survey Methodology

Background:

  • Accurate variance estimation is crucial for reliable statistical inference.
  • Traditional methods may lack efficiency when auxiliary information is limited.
  • Two-phase sampling offers a framework to incorporate auxiliary data.

Purpose of the Study:

  • To propose a novel variance estimator for two-phase sampling.
  • To enhance estimation efficiency using one auxiliary variable and one binary attribute.
  • To demonstrate the analytical and empirical superiority of the proposed estimator.

Main Methods:

  • Developed a novel variance estimator incorporating auxiliary information.
  • Derived theoretical properties including bias and Mean Squared Error (MSE).
  • Conducted simulation studies using health and education datasets.
  • Trained and evaluated machine learning classifiers (Regression Tree, Random Forest, Support Vector Regression).

Main Results:

  • The proposed estimator demonstrated analytical superiority with proven bias and MSE formulas.
  • Simulation results showed consistently lower MSE values compared to classical and competitive estimators.
  • Machine learning models showed good predictive power, but the proposed estimator offered better interpretability.
  • The three-parameter Weibull distribution was identified as most suitable for analysis.

Conclusions:

  • The novel variance estimator enhances estimation precision in two-phase sampling.
  • Minimal auxiliary information, structured sampling, and hybrid modeling improve variance estimation.
  • The proposed estimator provides a theoretically sound and empirically validated approach for applied studies.